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Lógica matemática/ ¬a→b,b→a,a→(c∧d),¬a,¬c,¬d

Expresión ¬a→b,b→a,a→(c∧d),¬a,¬c,¬d

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    Solución

    Ha introducido [src] 
    (Implies(~a, b), Implies(b, a), Implies(a, c & d), ~a, ~c, ~d)
    (Implies(Not(a), b), Implies(b, a), Implies(a, And(c, d)), Not(a), Not(c), Not(d))
    Solución detallada
    $$\neg a \Rightarrow b = a \vee b$$
    $$b \Rightarrow a = a \vee \neg b$$
    $$a \Rightarrow \left(c \wedge d\right) = \left(c \wedge d\right) \vee \neg a$$
    Simplificación [src]
    (Implies(Not(a), b), Implies(b, a), Implies(a, And(c, d)), Not(a), Not(c), Not(d)) 
    (Implies(~a, b), Implies(b, a), Implies(a, c & d), ~a, ~c, ~d)
    Tabla de verdad 
    +---+---+---+---+--------+
| a | b | c | d | result |
+===+===+===+===+========+
| 0 | 0 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 0 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 0 | 1 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 0 | 1 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 0 | 1 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 0 | 1      |
+---+---+---+---+--------+
| 1 | 1 | 1 | 1 | 1      |
+---+---+---+---+--------+
    FNC [src]
    (Implies(Not(a), b), Implies(b, a), Implies(a, And(c, d)), Not(a), Not(c), Not(d)) 
    (Implies(~a, b), Implies(b, a), Implies(a, c & d), ~a, ~c, ~d)
    FNCD [src]
    (Implies(Not(a), b), Implies(b, a), Implies(a, And(c, d)), Not(a), Not(c), Not(d)) 
    (Implies(~a, b), Implies(b, a), Implies(a, c & d), ~a, ~c, ~d)
    FNDP [src]
    (Implies(Not(a), b), Implies(b, a), Implies(a, And(c, d)), Not(a), Not(c), Not(d)) 
    (Implies(~a, b), Implies(b, a), Implies(a, c & d), ~a, ~c, ~d)
    FND [src]
    (Implies(Not(a), b), Implies(b, a), Implies(a, And(c, d)), Not(a), Not(c), Not(d)) 
    (Implies(~a, b), Implies(b, a), Implies(a, c & d), ~a, ~c, ~d)
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